Poisson cluster process (PCP) has recently been used as a tractable model for capturing the formation of user hot-spots in the stochastic geometry-based analyses of wireless networks[1]}, [2]}, [3]}, [4]}. As is usually the case in stochastic geometry, the contact and nearest-neighbor distance distributions play a crucial role in such analyses. Recall that the contact distance (CD) is the distance of the closest point of the point process (PP) from an arbitrary point (useful in characterizing the power of the serving link in cellular networks) and the nearest neighbor distance (NND) is the distance of the nearest neighbor from a typical point of the PP (which reflects the network connectivity). While distributions of both these distances are identical for a Poisson point process (PPP), it is not so in a PCP. The focus of this letter is on characterizing these distributions for an MCP, a special case of PCP, which has recently received attention because of its relevance in modeling user hot-spots (very similar models have also been used in 3GPP simulations [3]}).
